How do you find the value of the discriminant and determine the nature of the roots #5b^2+b-2=0#?

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Answer 1 · 2017-06-01T19:19:08

The discriminant is #41# and therefore there are 2 distinct real-number solutions.

If a quadratic equation is in the form:

#ax^2+bx+c#

The discriminant is defined to be:

#b^2-4ac#

#1^2-4(5)(-2)#

#1+40=41#

Since the discriminant is positive, there are 2 distinct real-number solutions.

If the discriminant is negative, there are no real-number solutions and if the discriminant is #0#, one repeated real-number solution.